That polynomial does not factor simply.
The roots of -13x^2+113x-22 = 0
are real numbers, since b^2 - 4 ac = 11625. The expression can be written
-13(x- A)(x-B), where A and B are
A = (-113 + sqrt 11625)/-26 = 0.19926
and
B = (-113 - sqrt 11625)/-26 = 8.49305